Definitely yes. That's my view.
I would say a monitor is an investment which you don't change time to time. There won't be much difference between 144hz & 240hz monitor, but a 240Hz monitor will give a competitive edge if you get one.
Now, I prefer to play competitive games at 1920x1080 to get the best & consistent frames as possible. However, 1440p brings better image quality due to more pixels and games are more of GPU-bound. This will change in future, as video cards are slowly making their way to 4K and even 8K. It will take some time to get a 1080p performance in 4k, by that time I consider 1440p 240hz will be a good choice.
Coming to your thoughts, Your video card can easily hit 200 frames or more in many first-person shooter games or FPP/TPP. So, it shouldn't be a problem if you get a 144Hz or 240Hz. Make sure you get a good display cable which will have higher bandwidth.